General Question

Where, exactly, is the intersection between Math and Patterns?

I enjoy math, but I’m not any good at it – my attention tends to throw its hands up in disgust when I actually make the ol’ brain work hard. I enjoy patterns, too, and those hold my attention longer so I’m pretty good with them. And I know that math and patterns are sort of hand-in-glove.

So I was wondering if there were a way to leverage my mad pattern skillz for mathematical purposes – or really, anything more interesting than laying tile. Which I’m pretty good at.

Speaking outside my realm of expertise here, and with all due respect to Gail, I see a great deal of overlap. Patterns mean some sort of regularity of relationship (unless you’re talking about patterns such as seeing crabs and archers when you look at the stars), and what is that but mathematics? You can generate a pattern from a formula and create a formula to describe a pattern.

Aren’t the patterns in numerical relationships a path to discovery of mathematical principles? And can’t those relationships typically be expressed graphically, whether by models, graphs, or abstract depictions?

As to how you might use the skill you have and its relationship to mathematics, I have no idea, but I’m sure there must be a way.

The mathematician’s pattern’s, like those of the painter’s or the poet’s, must be beautiful, the ideas, like the colours or the words, must fit together in a harmonious way. There is no permanent place in the world for ugly mathematics.

@Nullo What an excellent question. Maths deal well with place and pace, the first great leaps forward that maths made. The first math, developed by the ancient Greeks, was Geometry. It dealt with place. Then came Algebra and Calculus, which together were sufficient to deal with “pace”. No sequential math is sufficient to deal with an ever-changing pattern, however. Modeling the behavior of a hurricane, for instance, would not be possible without computer simulations that evolve to be ever more predictive.

For pattern, we need a whole new math that, unlike the previous two, is completely beyond the grasp of the current human brain. It can only be handled in massively parallel computing. There, you can take a truly junky collection of programs, feed them all the known data-points that might impact the pattern in question, and see which produce the most accurate predictions. Those, you then allow to “survive” along with mutated progeny. You repeat the process over and over. Bear in mind that in each iteration, you are crunching billions or trillions of complex equations. And generation after generation, the survival of the fittest few evolves an ever more accurate model. Brilliant as it may be, the human mind has nowhere near the raw processing power to do this. We can’t even fully comprehend what our simulations are doing. We just know roughly how well they work.

Nullo, one topic in math you may enjoy is that of sequences and series. Pattern-seeking abilities are absolutely invaluable here.

Say you have a sequence like 1, 3, 5, 7, 9… Anyone can understand intuitively what this is and where it is going, but not just anyone could give me an answer when I ask what the 1047th term in the sequence is. They might believe they have to actually list out 1047 terms in order to answer me. This is not necessary when you are a good pattern seeker. You can define this sequence with an expression involving n that, when substituting a value for n, will yield the nth term of the sequence. The expression for this particular example is 2n-1 (and the 1047th term is 2*1047–1 = 2093). All odd numbers are one less than an even number, and all even numbers are twice an integer. A good pattern seeker can see this far more easily than someone without that skill.

Of course that is a simple example. If you are interested and look into it further, things just get more fun from there.